December 27, 2011

“Tymoczko had discovered the fundamental geometric shape of two-note chords. They occupy the space of a Möbius strip, a two-dimensional surface embedded in a three-dimensional space. Music is not just something that can be heard, he realized. It has a shape.

He soon saw that he could transform more complex chords the same way. Three-note chords occupy a twisted three-dimensional space, and four-note chords live in a corresponding but impossible-to-visualize four-dimensional space. In fact, it worked for any number of notes — each chord inhabit ed a multidimensional space that twisted back on itself in unusual ways — a non-Euclidean space that does not adhere to the classical rules of geometry. A physicist friend told him that these odd multidimensional spaces were called orbifolds — a name chosen by the graduate students of Princeton mathematician William Thurston, who first described them in the 1970s. In the 1980s, physicists found a few applications for orbifolds in arcane areas of string theory. Now Tymoczko had discovered that music exists in a universe of orbifolds.”

A Grand Unified Theory of Music. I’m deep into writing the charts for this years’ show, and certainly believe that some kind of symmetry exists in all these notes. Of course, that could just be the result of blurry eyes.